EXCHANGE 


'dufx>ersit£  of  Cbicaao 


Intermediate  and  Complex  Ions*     V*     The 

Solubility  Product  and  Activity  of  The 

Ions  in  Bi-Bivalent  Salt 


A  DISSERTATION 

SUBMITTED  TO  THE  FACULTY  OF  THE  OGDEN  GRADUATE 

SCHOOL  OF  SCIENCE  IN  CANDIDACY  FOR  THE 

DEGREE  OF  DOCTOR  OF  PHILOSOPHY 

DEPARTMENT  OF  CHEMISTY 


BY 

H.  M.  PAINE 


Private  Edition  Distributed  by 
THE  UNIVERSITY  OF  CHICAGO  LIBRARIES 
CHICAGO,  ILLINOIS 


Reprinted  from  the  Journal  of  the  American  Chemical  Society  Vol.  XLI.  No.  8,  August,  1919. 


ZTbe  '(University  ot  Gbicaao 


Intermediate  and  Complex  Ions*     V*     The 

Solubility  Product  and  Activity  of  The 

Ions  in  Bi-Bivalent  Salt 


A  DISSERTATION 

SUBMITTED  TO  THE  FACULTY  OF  THE  OGDEN  GRADUATE 

SCHOOL  OF  SCIENCE  IN  CANDIDACY  FOR  THE 

DEGREE  OF  DOCTOR  OF  PHILOSOPHY 

DEPARTMENT  OF  CHEMISTY 


BY 

H.  M.  PAINE 


Private  Edition  Distributed  by 

.  THE  UNIVERSITY  OF  CHICAGO  LIBRARIES 
CHICAGO,  ILLINOIS 


Reprinted  from  the  Journal  of  the  American  Chemical  Society  Vol.  XLI.  No.  8,  August,  1919. 


EXCHANGE 


[Reprinted  from  a  paper  by  William  D.  Harkius  and  H.  M.  Paine.] 


INTERMEDIATE  AND  COMPLEX  IONS.     V.     THE   SOLUBILITY 

PRODUCT  AND  ACTIVITY  OF  THE  IONS  IN 

BI-BIVALENT  SALTS.1 

The  first  evidence  which  indicates  that  all  salts  which  give,  on  complete 
ionization,  3  or  more  ions,  ionize  in  steps  in  such  a  way  as  to  give  inter- 
mediate ions,  was  presented  by  Harkins2  in  1911.  The  earlier  idea  was 
that  intermediate  ions  are  present  in  aqueous  solution  of  some  of  the  salts 
of  higher  types,  but  not  in  all  cases.  Thus  Abegg  and  Spencer,3  in  1905, 
considered  that  thallous  oxalate  gives  rise  to  an  intermediate  ion,  but 
potassium  oxalate  does  not,  while  in  1911  Jellinek4  concluded  that  inter- 
mediate ions  are  present  in  solutions  of  sodium  sulfate,  but  not  when 
potassium  sulfate  is  the  solute.  Such  salts  are  mercuric  chloride,  cad- 
mium chloride,  and  lead  chloride  were  commonly  believed  to  give  inter- 
mediate ions,  but  the  more  ordinary  salts  were  in  general  supposed  to 
ionize  in  one  step  or  else  to  give  only  a  negligible  fraction  of  intermediate 
ions.  Perhaps  the  strongest  evidence  in  favor  of  ionization  in  one  step 

1  This  series  of  papers  was  begun  by  W.  D.  Harkins  in  the  Research  Laboratory 
of  Physical  Chemistry  of  the  Massachusetts  Institute  of  Technology  and  has  been 
continued  in  the  laboratory  of  the  University  of  Chicago  with  the  consent  of  Professor 
A.  A.  Noyes. 

2  J.  Am.  Chem.  Soc.,  33,  1836-72(1911);  Harkins  andPearce,  Ibid.,  37,  2679(1916). 

3  Z.  anorg.  Chem.,  46  406  (1905). 

4  Ibid.,  76,  309  (1911)- 


was  found  in  the  fact  that  in  solutions  of  uni-bivalent  salts  the  transference 
number  is  independent  of  the  concentration.  The  work  of  Harkins  in- 
dicates, however,  that  the  percentage  of  intermediate  ion  is  not  negligible, 
but  for  salts  of  the  type  of  potassium  sulfate  is  18%  for  o.oi  N  solutions, 
35%  at  o.  i  N,  and  rises  to  46%  in  a  normal  solution,  these  being  the  per- 
centages for  the  KSC>4~  ion. 

In  a  study  of  the  solubility  of  uni-bivalent  salts  it  was  found  that  whereas 
the  addition  of  a  salt  with  a  common  univalent  ion  decreases  the  solu- 
bility of  the  uni-bivalent  salt  very  greatly,  just  as  would  be  expected,  the 
addition  of  a  salt  with  a  common  bivalent  ion  has  an  entirely  different 
effect  from  what  had  previously  been  supposed.  In  other  words,  the 
solubility  curve  in  the  latter  case,  at  least  where  the  saturating  salt  has  a 
solubility  of  o .  05  N  or  more,  has  another  form  than  that  which  would  be 
predicted  from  the  solubility  product  principle  upon  the  basis  of  the  usual 
assumptions.  Instead  of  falling  rapidly  as  the  concentration  of  the  added 
salt  increases,  the  solubility  of  the  saturating  salt  decreases1  at  first  slightly 
but  then  increases. 

When  salts  of  the  bi-bivalent  type  are  used  as  saturating  salts  it  is  im- 
possible to  add  a  salt  with  a  common  univalent  ion;  but  when  salts  with 
bivalent  common  ions  are  added  to  solutions  of  calcium  sulfate  (see  Fig.  i), 
the  solubility  curves  have  somewhat  the  same  form  as  when  the  saturating 
salt  is  of  the  uni-bivalent  type.  The  explanation  given  by  Harkins  for 
the  peculiar  solubility  curve  of  the  uni-bivalent  salts,  was  that  it  is  due 
to  the  presence  in  such  solutions  of  a  considerable  percentage  of  inter- 
mediate ions  such  as  KSO4~,  BaCl+,  etc. 

It  was  found  that  the  presence  of  intermediate  ions  in  solution 
could  also  be  easily  recognized  from  the  slope  of  the  curve  representing 
the  solubility  of  the  un-ionized  part  of  the  saturating  salt  when  the  con- 
centration of  the  un-ionized  part  is  calculated  on  the  basis  of  the  usual 
assumptions,  which  are  as  follows:  (i)  That  the  isohydric  principle  is 
valid,  (2)  that  the  usual  method  of  calculating  percentages  ionization  is 
correct,  and  (3)  that  no  intermediate  ions  are  present  in  the  solution. 
Now,  it  happens  that  the  deductions  obtained  by  this  method  of  detecting 
intermediate  ions  hold  in  all  probability  even  if  (i),  the  isohydric  principle 
is  not  valid,  and  (2)  if  the  usual  method  of  calculating  the  percentage 
ionization  is  incorrect.  This  is  true  because  no  use  is  made  of  the  abso- 
lute values  of  the  solubility  of  the  un-ionized  part  of  the  salt  as  calculated, 
and  the  only  essential  feature  of  the  method  is  a  proper  comparison  of 
the  slopes  of  the  calculated  solubility  curves  for  the  non-ionized  parts  of 
uni-univalent  and  uni-bivalent  salts.  Thus,  when  calculated  in  the  usual 

1  In  the  case  of  highly  soluble  salts  of  this  type  this  initial  decrease  is  absent, 
and  the  curves  have  the  form  which  would  be  expected  if  the  added  salt  had  no  ion  in 
common  with  the  saturating  salt. 


way,  such  curves  for  the  uni-univalent  salts  slope  rapidly  downward  as 
the  total  ion  concentration  (or  the  concentration  of  the  added  salt)  in- 
creases. Now,  if  similar  curves  are  constructed  for  uni-bivalent  salts,  it 
might  be  expected  that  they  would  have  a  somewhat  similar  form,  and 
this  is  exactly  what  is  found  when  the  added  salts  used  are  such  as  would 
have  little  effect  upon  the  calculated  solubility  of  the  un-ionized  part  when 
intermediate  ions  are  present.  The  only  salts  of  this  kind  are  those  with  no 
-common  ion.  In  this  case  the  curves  for  uni-univalent  and  uni-bivalent  salts 
lie  almost  exactly  parallel  (compare  with  Fig.  3).  However,  when  the 
added  salt  contains  a  common  bivalent  ion,  the  curves,  when  calculated 
on  the  basis  of  the  third  assumption,  i.  e.,  that  no  intermediate  ions  are 
present,  should  not  show  the  same  slope  if  intermediate  ions  are  present 
in  considerable  quantity.  From  the  change  in  the  slope  of  the  curve  it 
would  be  possible  to  form  some  idea  of  the  amount  of  the  intermediate 
ion  present,  although  a  quantitative  estimate  can  be  made  much  more 
accurately  by  the  use  of  other  methods.  Now,  if  intermediate  ions  are 
present  in  the  saturating  salt,  the  calculated  solubility  of  the  un-ionized 
part  should  decrease  much  more  rapidly  when  the  added  salt  contains  a 
common  univalent  ion,  and,  on  the  other  hand,  when  a  salt  containing  a 
common  bivalent  ion  is  added,  this  solubility  should  either  decrease  less 
rapidly  or  if  the  relative  number  of  intermediate  ions  is  large,  the  calcu- 
lated solubility  curve  should  rise  instead  of  falling,  and  this  latter  has 
been  found  to  be  the  case  for  uni-bivalent  salts.  It  will  be  seen  that  this 
method  of  showing  the  presence  of  intermediate  ions,  and  also  something 
of  their  relative  amount,  depends  upon  the  deviation  of  the  calculated 
solubility  curves  from  the  normal  slope,  since  at  least  the  greater  part  of 
the  deviation  is  caused  by  the  false  assumption  that  intermediate  ions  are 
absent. 

When  it  is  realized  that  more  than  half  of  the  salts  commonly  used  are 
higher  type  salts,  it  will  be  seen  that  it  is  important  to  extend  this  in- 
vestigation to  a  study  of  types  still  higher  than  the  uni-bivalent  type  al- 
ready studied. l  The  next  most  important  type  of  salts  is  the  bi-bivalent ; 
and  in  this  type  of  salts  there  is  a  reversion  from  the  tri-ionic 
salts  previously  investigated  to  di-ionic  salts,  which,  with  respect  to  the 
number  of  ions  formed  by  a  simple  ionization,  would  seem  to  belong  to 
the  same  type  as  the  di-ionic  uni-univalent  salts.  Since,  by  their  simple 
ionization  the  bi-bivalent  salts  would  give  the  same  number  of  ions  per 
molecule  it  might  be  expected  that  the  curve  for  the  solubility  of  the  un- 
ionized part  should  be  of  the  same  general  form  as  for  the  uni-univalent 
salts,  provided  that  the  ionization  of  the  bi-bivalent  salts  is  entirely  a 
simple  one. 

1  Harkins  and  Pearce,  J.  Am.  Chem.  Soc.,  37,  2679  (1916)  have  shown  that  uni-triv- 
alent  salts  give  a  large  number  of  intermediate  ions  in  solution. 


6 

In  view  of  these  interesting  ionization  relations  of  trionic  and  still  higher 
type  salts,  a  study  of  sparingly  soluble  bivalent  salts  was  undertaken 
with  calcium  sulfate  as  a  type  salt  of  this  group.  Its  solubility  and  con- 
ductance were  determined  in  pure  water  and  also  in  solutions  of  various 
concentrations  of  copper  sulfate,  magnesium  sulfate,  and  potassium  ni- 
trate. Density  determinations  were  made  on  all  mixtures  and  all  weigh- 
ings were  corrected  to  vacuum.  In  the  calculations  the  atomic  weights 
for  1910  were  used. 

Preparation  of  Salts  and  Solutions. 

The  water  used  for  this  investigation  had  in  no  case  a  greater  specific  conductance 
than  0.7  X  io~6  and  the  average  value  in  the  bottles  in  which  it  was  stored  was 
0.6  X  io~6. 

Calcium  Sulfate. — This  salt  was  made  by  the  addition  of  a  very  dilute  potassium 
sulfate  solution  to  to  very  dilute  calcium  chloride  solution.  Kahlbaum's  "Zur  Analyse" 
salts  were  used  and  the  work  carried  out  in  special  vessels  of  resistance  glass.  The 
calcium  sulfate  was  washed  thoroughly  and  rotated  with  several  successive  portions 
until  the  conductivity  became  constant.  This  salt  was  preserved  in  glass-stoppered 
resistance  glass  bottles. 

Gypsum. — For  comparison  some  very  clear  plates  of  gypsum  were  obtained  from 
Dr.  A.  D.  Brokaw  of  the  Geology  Department. 

Magnesium  Sulfate — Kahlbaum's  "Zur  Analyse"  salt  was  twice  recrystallized 
from  conductivity  water  and  a  stock  solution  made  up  and  analyzed  by  evaporation  in 
platinum  and  weighing  as  magnesium  sulfate. 

Copper  Sulfate. — Kahlbaum's  "Zur  Analyse"  salt  was  twice  recrystallized  from 
conductivity  water. 

Potassium  Nitrate. — Baker's  potassium  nitrate  was  recrystallized  twice  from 
conductivity  water. 

Methods  of  Analysis. 

Calcium. — Calcium  was  determined  by  careful  precipitation  with  ammonium 
oxalate  from  ho:  solution;  after  standing  4-6  hours,  the  calcium  oxalate  was  filtered, 
washed  with  water  containing  a  little  ammonium  oxalate,  ignited  in  tared  platinum 
crucibles  and  weighed  as  calcium  oxide.  Where  copper  was  present  it  was  removed 
from  a  very  dilute  solution  by  precipitation  with  hydrogen  sulfide.  The  separation 
of  magnesium  from  calcium  presented  difficulties  because  of  the  well-known  fact  that 
the  quantitative  separation  of  small  amounts  of  calcium  from  much  larger  amounts  of 
magnesium  is  unsatisfactory.  The  method  proposed  by  Cameron  and  Bell1  leaves 
much  to  be  desired  from  th  standpoint  of  accuracy.  A  plate  of  pure  gypsum  rotated 
in  25  cc.  of  conductivity  water  showed  a  loss  equivalent  to  solubility  of  2.067  S- 
per  1000  g.  solution.  The  solution  from  this  gave  2.083  g.  CaSO*  per  1000  g.  of  solu- 
tion by  the  oxalate  method,  while  the  specific  conductance  was  0.0022115  ohms,  almost 
the  same  as  tha  for  the  prepared  salt  (0.0022148).  This  method  was  used  therefore 
only  in  solutions  of  comparatively  high  con  entration  of  magnesium  sulfate.  For 
the  more  dilute  solutions  the  method  proposed  by  Richards,  McCafTery  and  Bisbee2 
was  used. 

Experimental  Methods. 

An  excess  of  the  calcium  sulfate  was  rotated  with  water  or  solution  of  a  salt  in  a 
500  cc.  glass  stoppered  resistance  glass  bottle  which  had  been  "steamed  out"  and 

1  J.  Phys.  Chem.,  10,  212  (1906). 

2  Proc.  Am.  Acad ,  36,  375  (1901). 


thoroughly  seasoned.  The  temperature  was  measured  by  a  thermometer  which  had 
been  compared  with  a  certified  Baudin  thermometer.  For  each  determination  satura- 
tion was  approached  both  from  under-saturation  and  supersaturation.  The  solutions 
were  filtered  in  the  thermostat  and  the  first  50  cc.  rejected,  in  order  to  prevent  errors 
due  to  adsorption.  In  the  experiments  with  copper  sulfate  the  concentration  of  copper 
was  determined  for  each  bottle  separately.  In  the  other  series  solutions  were  care- 
fully made  up  in  calibrated  flasks  from  a  weighed  amount  of  standard  solution.  The 
calcium  sulfate  was  finally  carefully  washed  on  a  platinum  cone  with  a  large  amount 
of  the  solution,  and  quickly  transferred  to  the  bottle,  which  was  then  filled  up  with  solu- 
tion and  rotated  as  usual. 

The  conductivity  measurements  were  made  in  the  usual  way  with  a  roller  bridge 
carefully  standardized.  The  apparatus  was  similar  to  that  used  by  Washburn.1  Great 
care  was  taken  throughout  the  work  to  exclude  carbon  dioxide  from  the  solutions. 
The  bottles  were  all  filled  with  carbon  dioxide-free  air  and  all  solutions  and  water 
carefully  protected  from  contact  with  the  air  by  soda  lime  trains. 

Experimental  Data. 

The  results  of  the  solubility  determinations  of  calcium  sulfate  in  solu- 
tions of  copper  sulfate  are  given  below  in  Table  I,  in  Potassium  nitrate  in 
Table  Ha,  in  magnesium  sulfate  in  Table  116,  and  those  for  gypsum  in 
magnesium  sulfate  in  Table  lie. 

The  solubility  of  calcium  sulfate  in  solutions  of  copper  sulfate,  magne- 
sium sulfate,  and  potassium  nitrate,  together  with  the  conductances  of 
all  of  the  solutions  of  the  pure  salts  and  of  the  mixtures,  were  determined 
by  us,  because  none  of  the  previous  work  on  calcium  sulfate  gave  exten- 
sive enough  conductivity  data  for  our  purpose.  The  solubility  data  are 
plotted  as  undotted  lines  in  Fig.  i,  while  the  dotted  lines  represent  the 
work  of  Cameron  with  potassium  and  sodium  sulfates  as  the  added  salts. 
Other  data  of  a  similar  nature  may  be  found  in  papers  by  Sullivan2  and  by 
Cameron3  and  his  associates. 

The  curves  in  this  figure,  which  represent  the  addition  of  the  common 
bivalent  ions,  do  not  have  the  form  to  be  expected  when  a  common  ion 
is  added,  in  fact,  as  is  shown  most  clearly  in  Fig.  i,  at  a  very  low  concen- 
tration (0.15  AT)  the  copper  sulfate  curve  changes  to  the  form  to  be  ex- 
pected when  a  salt  with  no  common  ion  is  added,  while  that  for  magnesium 
sulfate  changes  at  about  0.35  N.  The  form  of  these  curves  is  somewhat 
the  same  as  that  previously  found  when  a  salt  with  a  common  bivalent 
ion  is  added  to  a  solution  in  which  the  saturating  salt  is  unibivalent  and 
has  a  solubility  of  0.07  N  or  more.  The  principal  difference  is  that  the 
initial  solubility  drop  is  greater  in  the  case  of  the  bi-bivalent  salts.  This 
change  in  the  form  of  the  curves  representing  the  common  ion  effect  has 

1  J.  Am.  Chem.  Soc.,  35,  177  (1913). 

2  Ibid.,  27,  532  (1905). 

8  Cameron  and  Seidell,  J.  Phys.  Chem.,  5,  643-55  (1901);  Cameron,  Ibid.,  5, 
56  (i  01);  Seidell  and  Smith,  Ibid.,  8,  493  (1904);  Cameron  and  Bell,  J.  Am.  Chem. 
Soc.,  28,  1220  (1906);  Cameron  and  Bell,  J.  Phys.  Chem.,  10,  212  (1906);  Cameron  and 
Brezeale,  Ibid.,  8,  337-40  '1904). 


3*0000000 


a—  to  N    cj    PJ    cj    t 

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9 

TABLE  III. — EQUIVALENT  CONDUCTANCE  OF  MAGNESIUM  SULFATE  AT  18°  AND  AT  25°. 

(CONCENTRATIONS  IN  EQUIVALENTS  PER  LITER,  CONDUCTANCE 

IN  RECIPROCAL  OHMS.) 


Concentration. 

Al8°.                         A/A0. 

A25°. 

A/AO. 

O.OO 

135.0                loo.oo 

114.4 

100.00 

0.00050635 

i  3-3                   91-33 

104.7 

91-52 

o.ooiO"47 

117.4                   86.96 

XOO.I 

87.50 

0.0020094 

i  10.  8                   82.08 

91-67 

82.75 

0.005023 

99-o                   73.33 

84-35 

73-73 

0.010047 

88.85                 65.82 

76.15 

66.56 

0.020094 

78.98                 58.50 

67.23 

58.77 

0.050235 

66  .05                  48  .  93 

56.54 

49  37 

0.10047 

57-79                 42.81 

49.58 

43-34 

o  .  20094 

49.82                  36.90 

43-12 

37.69 

0.50235 

40.72                  30.16 

35.25 

30.81 

1.0067 

33-37                  24.72 

28.81 

25.18 

TABLE  IV.—  CONDUCTANCE  OF  CALCIUM  SULPATE  SOLUTIONS. 

(a)  AT  25°. 

Equivalents 

Specific  conduc-                A. 

H25 

per  liter  X  10».     tance  X  10*.    I/ohm.       I/ohm. 

A/A*. 

U4  • 

O.O 

I4O.O 

100.00 

0.099955 

1.3657                    136.63 

97-59 

0.19955 

2.650                      132.88 

94.91 

0-49795 

6-343                      127.38 

90.98 

0-9959 

12.104                      121.57 

86.84 

1-9975 

22.612                         I3.2O 

80.86 

0.99720 

5.011 

50.195                loo  15 

71-53 

0.99748 

10.081 

90.17                            89.45 

63.89 

0.99782 

30.610 

221.48                            72.35 

51-68 

0.99911 

36  .  408 

252.0                               69.21 

49-44 

(Hulett) 

(6)  AT   18°. 

d}8. 

0.0 

119.00 

100.00 

0.10013 

1.1644            116.28 

97-80 

0.19986 

2.2670              113.43 

95.32 

0.49871 

5.436            109.0 

91.60 

0-99755 

10.407                103.82 

87.24 

2.007 

19.446              97.19 

81.67 

5-023 

43.270                  86.20 

72-44 

0.99895 

10.096 

77.96                    77.21 

64.88 

0.99897 

TABLE  V.—  CONDUCTANCE  OF  COPPER  SULFATB  SOLUTIONS 

AT  25°. 

Equivalent 
concentration 

Specific  conduc- 
tance X  10»     I/ohm. 

A. 

I/ohm 

,25 
04  ' 

0.025156 

1.7286 

86.50                   o. 

99950 

o  .  050202 

2.9688 

59  13                     I- 

0013 

o.  100081 

5-0609 

50.56                     i. 

0053 

0.201085 

8.7545 

43-53                      I- 

0136 

0.41993 

15-535 

36.99                      I- 

0307 

1-9335 

46  .  082 

23-83                      I. 

14645 

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11 


been  shown,  in  previous  papers  of  this  series,  to  be  connected  with  the 
formation  of  complex  ions,  double  salts,  or  intermediate  ions. 

Another  indication  of  the  presence  of  intermediate  or  complex  ions  is 
that  the  solubility  product  as  calculated  from  the  solubility  measurements 
increases  more  rapidly  than  when  such  ions  are  absent.  This  is  because 
the  calculations  of  the  ionization  count  a  part  of  the  material  present  as 
intermediate,  as  being  in  the  form  of  simple  ions,  and  since  the  concen- 
tration of  the  intermediate  ion  increases  rapidly  with  the  concentration, 


0.04 


o.o 


0.0 


0.2 


1.6 


2.0 


0.4        0.6        o.8        i  .o        1.2         1.4 

Equivalents  per  liter  of  added  salt. 

Fig.  i. — Solubility  of  calcium  sulfate  in  solutions  of  other  salts.  Note  that  the  solu- 
bility decrease  when  the  concentration  of  the  added  salt  is  only  o.  i  equiva- 
lents is  very  much  less  than  corresponds  to  the  solubility-product  principle. 
At  higher  concentrations  the  curves  take  on  the  form  of  non-common  ion 
curves. 

this  leads  to  an  apparent  rapid  increase  of  the  solubility  product.  It 
has  been  shown  in  a  former  paper  that  when  account  is  taken  of  the  in- 
termediate ions  in  solutions  of  uni-bivalent  salts,  the  solubility  product 
as  calculated  becomes  much  more  constant.  Fig.  2  indicates  that  the  solu- 
bility product  of  a  bi-bivalent  salt,  calculated  on  the  usual  assumption 
that  intermediate  and  complex  ions  are  absent,  increases  with  extreme 
rapidity  as  the  concentration  of  the  solution  (the  total  ion  concentra- 
tion) increases.  Thus,  when  copper  sulfate  is  the  added  salt,  the  solu- 


12 

bility  product  is  increased  to  more  than  3  times  its  smallest  value  before 
the  total  ion  concentration  has  reached  o .  i  N,  so  the  apparent  activity 
of  the  bivalent  ions  decreases  very  rapidly  with  increasing  ion  concentra- 
tion. It  is,  of  course,  possible  that  the  whole  of  such  a  very  rapid  increase 


o.o 

20  40  60  80  ioo  120 

Total  ion  concentration  (S*)  in  milli-equivalents. 

Fig.  2. — The  solubility   product  for   uni-univalent,  uni-bivalent,  and  bi-bivalent  salts, 
calculated  on  the  assumption  that  intermediate  ions  are  absent. 

in  the  solubility  product  of  salts  of  this  class,  cannot  be  explained  by  the 
assumption  of  the  existence  of  complex  ions. 

The  solubility  of  the  un-ionized  part  of  the  salt  as  calculated  on  the  as- 
sumption that  intermediate  ions  and  other  complexes  are  absent  (Fig.  3) 
is  much  more  constant  than  it  was  found  to  be  for  uni-uni-  and  uni-bi- 


13 


valent  salts,  except  in  the  more  concentrated  solutions  in  which  copper 
sulfate  is  the  added  salt.  The  change  in  the  slope  of  these  curves  as  com- 
pared with  those  for  the  uni-univalent  salts,  is  in  the  same  direction  as 
that  for  uni-bivalent  salts  when  the  common  bivalent  ion  is  added,  that  is 
the  change  in  slope  is  in  the  direction  to  be  expected  if  intermediate  ions 
are  present. 


0.4 


i.o 


1.2 


2.0 


1.4  1.6 

Log.1  total  ion  concentration  Z*. 

Concentrations  in  milli-equivalents. 

Fig-  3- — The  concentration  of  the  un-ionized  part  of  uni-univalent  (T1C1),  uni-bivalent 
(Ba(IO,)2,  Ba(BrO3)2,  Ag2SO4f  PbCl2)  and  bi-bivalent  (CaSO<)  salts  in  their 
saturated  solutions  in  the  presence  of  other  salts,  calculated  on  the  in- 
correct consumption  that  intermediate  ions  are  absent. 

1  The  curves  for  barium  iodate  should  be  ten  squares  lower  down  and  five  squares 
further  to  the  left.  Note  how  closely  these  curves  parallel  those  for  barium  bromate  in 
spite  of  their  large  displacement. 


14 

It  is  to  be  specially  noted  that  most  of  the  results  described  above  were  ob- 
tained in  dilute  solutions,  that  is  below  o.i  N  total  ion  concentration, 
and  that  therefore  they  are  not  to  be  considered  from  the  standpoint  of 
much  of  the  work  in  the  literature  in  regard  to  the  formation  of  double 
or  complex  salts  in  concentrated  solutions.  The  formation  of  these 
latter  double  and  complex  salts  is  highly  specific,  while  that  for  which 
evidence  is  obtained  in  this  paper  will  undoubtedly  be  found  to  be  gen- 
eral, just  as  the  similar  behavior  of  uni-bivalent  salts  described  in  the  first 
paper  of  this  series,  was  later  proved  to  be  perfectly  general. 

As  has  been  suggested  in  the  first  part  of  this  paper,  a  large  part  of  this 
abnormal  behavior  of  bi-bivalent  salts  would  be  only  apparent  if  complex 
bivalent  ions  are  formed.  These  would  have  the  form 

/SO4~  /Ca+  /Ca+  /Ca  + 

Ca<  SO/  SO/  SO/ 

VN/Trr  + 


/Mg  +  /Cu  +  /SO4~  /SO4~  /SO4K 

so/  so/  Mg<(  a/  cu<( 

XMg  +  \Zu+  XSO4-  XSO4-  XS04~ 

and  would  form  salts  of  a  ring  structure: 

/SO4\  /SO4\  /SO4v  /SO4K 

Ca<^         yCa  Cu<^         yCa  Q/         yCu  Cu<^  etc. 

\crj  /  \<?r> '  NQfl  r  \Qr»  v 

o<J4  Ow4  ow4  oU4Js. 

Since  the  formation  of  such  intermediate  ions  or  ring  or  double  salts 
stores  the  materials  in  forms  in  which  they  do  not  enter  into  the  primary 
equilibrium  between  the  solid,  the  un-ionized  part  of  the  salt  consisting 
of  single  molecules,  and  the  ordinary  ions,1  it  increases  what  is  called  the 
solubility  of  the  salt  by  approximately  the  amount  of  the  material  put 
into  such  forms.  This  is  similar  to  the  increase  in  the  solubility  of  a  salt 
by  metathesis.  The  complex  ions  do  not  enter  into  the  simple  solubility 
product  equilibrium,  as  it  actually  is,  but  since  they  carry  the  current, 
they  make  the  apparent  number  of  simple  ions  greater  than  accords  with 
the  facts,  so  that  the  solubility  product  calculated  on  the  basis  of  the  ap- 
parent number  instead  of  the  real  number  of  simple  ions,  comes  out  too 
large,  and  since  the  number  of  intermediate  ions  increases  rapidly  with 
the  concentration,  the  apparent  solubility  product,  also  increases  very 
rapidly. 

The  equivalent  solubility  S0  of  a  salt  which  dissociates  in  the  above 
manner  may  be  given  as  follows: 

S0  =  2(AB)0  +  4(^2^2)0  +  2(50)  +  z(ABA)0  +  ^(BAB)01 
where  AB  represents  the  number  of  mols  of  the  un-ionized  single  mole- 

1  When  this  series  of  researches  was  begun  in  1910  it  was  the  intention  to  investi- 
gate complex  formation  in  salts  of  the  uni-univalent  type.  Since  that  time  this  prob- 
lem has  been  taken  up  by  G.  McP.  Smith  and  his  students  in  a  series  of  comprehen- 
sive studies.  See  /.  Am.  Chem.  Soc.,  40,  1802  (1918). 


15 

cules,  AzBz  of  the  double  molecules,  B  of  the  positive  ion,  ABA  of  the 
negative  intermediate  ion,  and  BAB  of  the  positive  intermediate  ion.  A 
more  complete  analysis  for  the  similar  case  of  a  uni-bivalent  salt  has  al- 
ready been  given  in  a  former  paper  of  this  series.1 

In  solutions  of  uni-bivalent  salts,  in  addition  to  intermediate  ions  such 
as  KSO4~,  ions  of  the  type  of  K-SO4-SO4~  are  to  be  expected,  while  in 
concentrated  solutions  of  uni-univalent  salts,  there  is  much  probability 
that  double  molecules  such  as  K2C12,  and  their  complex  or  intermediate 
ions,  K2C1+  and  KC12"  exist.1 

While  the  evidence  for  the  existence  of  complex  ions  in  solutions  of 
bi-bivalent  salts  is  neither  so  complete  or  so  perfect  as  that  obtained  in 
solutions  of  uni-bivalent  salts  from  the  standpoint  of  the  solubility  re- 
sults obtained  thus  far,  there  is  an  independent  line  of  evidence  which 
could  not  be  obtained  in  the  latter  case  ;  that  is  the  mobility  of  the  ions  in 
bi-bivalent  salt  solutions  decreases  rapidly  as  the  concentration  of  the  solu- 
tion increases.  This  change  is  in  the  direction  to  be  expected  if  complex 
ions  are  present.  Such  complex  ions  differ  from  the  complex  ions  usually 
considered  in  the  literature  in  that  the  evidence  points  to  their  existence 
in  dilute  solutions,  just  as  is  the  case  with  intermediate  ions.  In  this  re- 
spect the  complex  ions  considered  in  this  paper  are  more  like  such  inter- 
mediate ions  ;  and  so  might  well  be  called  intermediate  ions,  since  they  are 
intermediate  between  the  single  and  the  double  molecules  of  the  salt. 

Summary. 

1.  It  has  been  shown  in  former  papers  by  Harkins  and  his  co-workers 
that  salts  of  the  tri-ionic  and  still  higher  types  ionize  in  steps  and  give, 
even  in  o  .  i  or  o  .  i  N  solutions,  a  very  considerable  percentage  of  inter- 
mediate ions.     The  present  paper  shows  that  the  solubility  relations  of 
calcium  sulfate  when  common  ions  are  added,  are  very  similar  to  those 
of  such  higher  type  salts.     This  indicates  the  probability  that  complex 
ions,  such  as  Ca(SO4)2        and  Ca2SO4+~f  are  present  in  the  solutions. 
These  complex  ions  differ  from  what  are  usually  considered  under  this 
designation,  since  they  are  present  to  a  considerable  extent  in  dilute  solu- 
tions, so  in  this  sense  they  are  more  like  intermediate  ions. 

2.  If  it  is  assumed  that  such  complex  ions  are  absent,  the  solubility  prod- 

1  According  to  the  octet  theory  of  Lewis,  lately  amplified  by  Langmuir,  these 

O        O 


X)—  S—  Ov 

salts  would  have  the  structure  Ca<^  yCa  where  each  bond  represents  a  pair 

X)—  S—  (X 


O        O 

of  electrons,  common  to  two  octets. 


16 

uct  calculated  on  this  basis  is  found  to  increase  with  great  rapidity  as  the 
concentration  increases;  thus,  if  the  total  ion  concentration  increases 
from  0.02  to  o.io  N  the  solubility  product  is  tripled,  so,  if  only  simple 
ions  are  present  their  activity  decreases  very  rapidly  with  an  increase  in 
concentration.  On  the  other  hand,  the  solubility  found  for  the  un-ionized 
part  on  the  basis  of  this  assumption,  remains  much  more  constant  than  in 
the  case  of  uni-univalent  salts.  The  change  in  the  slope  of  these  curves 
is  in  the  direction  which  is  to  be  expected  if  complex  ions  are  present. 

3.  The  percentage  concentration  of  such  complexes  is  much  higher  in 
copper  sulfate  than  in  magnesium  sulfate  solutions,  at  the  lower  concen- 
trations. 


OCT 
OCT  15 

OCT  29  1937 


JUN 

;RY  USE 


Gaylord  Bros. 

Makers 
Syracuse,  N.  Y. 

PAT.  JAN  21,  1908 


P3 


-  DIVERSITY  OF  CALIFORNIA  LIBRARY 


"iiiiii^ 


